Question

use euclid's division algorithm to find the HCF of - -
i.) 4052 and 10576
ii.) 210 and 55

Answer 1

1. 4052 and 10576

We have,

4052<10576

Using Euclid's division algorithm

10576=4052×2+2472

So remainder is not equal to 0

Using Euclid's division algorithm

4052=2472×1+1580

So remainder is not equal to 0

Using Euclid's division algorithm

2472=1580×1+892

So remainder is not equal to 0

Using Euclid's division algorithm

1580=892×1+688

So remainder is not equal to 0

Using Euclid's division algorithm

892=688×1+204

So remainder is not equal to 0

Using Euclid's division algorithm

688=204×3+76

So remainder is not equal to 0

Using Euclid's division algorithm

204=76×2+52

So remainder is not equal to 0

Using Euclid's division algorithm

76=52×1+24

So remainder is not equal to 0

Using Euclid's division algorithm

52=24×2+4

So remainder is not equal to 0

Using Euclid's division algorithm

24=4+6+0

So remainder is equal to 0

Therefore HCF= 4

2. 210 and 55

We have,

210 >55

Using Euclid's division algorithm

210=55×3+45

So remainder is not equal to 0

Using Euclid's division algorithm

55=45×1+10

So remainder is not equal to 0

Using Euclid's division algorithm

45=10×4+5

So remainder is not equal to 0

Using Euclid's division algorithm

10=5×2+0

So remainder is equal to 0

Therefore HCF= 5
Hope it helps!